The entity(ies) that keep causing the "random" phenomena with the Social Studies Club kids name themselves Heartseed. Sometimes translated as the linked plant genus. Even Wikipedia editors seem to have gone in the same train of thought. But that seems to be speculation.
But since the whole series is about connecting their hearts, it could be the case that they are really heart (as in a human's emotion-holding "organ" in popular culture) seeds.
Are they plant-ish, really?